On ZpZp[u, v]-additive cyclic and constacyclic codes

Let $\mathbb{Z}_{p}$ be the ring of residue classes modulo a prime $p$. The $\mathbb{Z}_{p}\mathbb{Z}_{p}[u,v]$-additive cyclic codes of length $(\alpha,\beta)$ is identify as $\mathbb{Z}_{p}[u,v][x]$-submodule of $\mathbb{Z}_{p}[x]/\langle x^{\alpha}-1\rangle \times \mathbb{Z}_{p}[u,v][x]/\langle x^{\beta}-1\rangle$ where $\mathbb{Z}_{p}[u,v]=\mathbb{Z}_{p}+u\mathbb{Z}_{p}+v\mathbb{Z}_{p}$ with $u^{2}=v^{2}=uv=vu=0$. In this article, we obtain the complete sets of generator polynomials, minimal generating sets for cyclic codes with length $\beta$ over $\mathbb{Z}_{p}[u,v]$ and $\mathbb{Z}_{p}\mathbb{Z}_{p}[u,v]$-additive cyclic codes with length $(\alpha,\beta)$ respectively. We show that the Gray image of $\mathbb{Z}_{p}\mathbb{Z}_{p}[u,v]$-additive cyclic code with length $(\alpha,\beta)$ is either a QC code of length $4\alpha$ with index $4$ or a generalized QC code of length $(\alpha,3\beta)$ over $\mathbb{Z}_{p}$. Moreover, some structural properties like generating polynomials, minimal generating sets of $\mathbb{Z}_{p}\mathbb{Z}_{p}[u,v]$-additive constacyclic code with length $(\alpha,p-1)$ are determined.Comment: It is submitted to the journa

Elastic plastic fracture behavior and effect of band- overload on fatigue crack growth rate of an HSLA steel

Study of fracture toughness and fatigue crack growth behavior are important parameters of structural materials. These parameters can be used to predict their life, service reliability and operational safety in different conditions. The material used in this investigation is an HSLA steel. In the first part of this investigation elastic plastic fracture toughness (JIc and äIc) were measured, by resistance curve method. Tests were carried out on CT specimens, using unloading compliance technique. These tests were conducted at three different displacement rates. It is observed that fracture toughness decrease with increasing rate of displacement. In the next part of this investigation effect of single overload and band-overload on fatigue crack growth of same steel were studied. These tests were conducted on CT specimens. Single overload and band overloads were applied under mode-I condition, during constant amplitude (tension-tension) fatigue crack growth test. It is observed that overload and band-overload applications resulted retardation on the fatigue crack growth rate in most of the cases. It is also noticed that maximum retardation took place on application of seven successive overload cycles